This project develops the theory of linkage disequilibrium (LD) estimation for a pair of genetic markers using the maximum likelihood function of a multinomial distribution. Basic statistics for LD such as $D$, $D'$ and $r^2$ are discussed. The objective is to apply the theoretical analysis to a database that contains observed genotype data of 1685 markers from 146 individuals presumably related to colon cancer. A descriptive analysis of this dataset is presented, together with a detailed LD study of it. The results reveal a clear LD block structure of the dataset and a high association between consecutive markers. The last part of the thesis gives an example of how to take advantage of this structure by testing association between one LD block and colon cancer. The free software environment R is used to perform all the statistical computations.